The Knicks made a foray into the Omer Asik sweepstakes and had discussions with the Rockets and a third team about a three-way swap, an NBA source told The Post. But the source said the Knicks are likely to fall short of obtaining the Houston 7-footer who has asked to be traded.

Asik, who makes $5.5 million this season, is an obvious fit as the Knicks are thin and injury-wracked up front with Kenyon Martin and Amar’e Stoudemire both risks, but have a glut of shooting guards. The Knicks are willing to deal Iman Shumpert — whose stock has fallen a bit in recent weeks — and Metta World Peace. J.R. Smith is the lone prominent Knick who can’t be traded until Jan. 15 under a quirk in the collective bargaining agreement.

The Rockets want to move Asik by Thursday, the deadline when players obtained in a trade can still be moved again at February’s trade deadline. Yahoo! Sports has reported Philadelphia, Atlanta, Boston and Cleveland are frontrunners for Asik.